Carleman-Vekua equation with a singular point

TL;DR

This paper proves the unconditional solvability of the Carleman-Vekua equation with a singular point, solves the associated Riemann-Hilbert problem, and characterizes the zeros and poles of solutions.

Contribution

It establishes new solvability results and solution representations for the Carleman-Vekua equation with a singular point, advancing understanding of its analytical structure.

Findings

Unconditional solvability of the equation is proved.

Integral representations of solutions are derived.

Zeros and poles of solutions are characterized.

Abstract

In this article uncoditional solvability of the Carleman-Vekua equation with a singular point is proved, the Riemann-Hilbert problem is solved integral representations of solutions, the strictures of their zeros and poles are recieved.